**Optymalizacja kształtu dynamicznych zagadnień kontaktowych**

*Andrzej Myśliński*

This paper deals with the numerical solution of a shape optimization problem of a viscoelastic body in unilateral dynamic contact with a rigid foundation The heat generation due to friction is taken into account. The shape optimization problem consists in finding, in a contact region, such a shape of the boundary of the domain occupied by the body that the normal contact stress is minimized. The volume of the body is assumed constant. In this paper, the necessary optimality condition for this optimization problem is formulated. Numerical algorithm for solving the optimal conditions system for this optimization problem is based on application of the level set methods. The speed vector field driving the propagation of the level set function is given by the Eulerian derivative of an appropriately defined functional with respect to the free boundary. The Eulerian derivative is calculated using the material derivative approach. Numerical examples are provided.

**Słowa kluczowe:** *level set methods, shape optimization,
dynamic contact problem*